14 Jul
2007
14 Jul
'07
6:48 p.m.
On 7/14/07, Fred lunnon <fred.lunnon@gmail.com> wrote
I ought to have mentioned that if a spherical triangle has sides a,b,c and angles A,B,C, then its dual is the triangle with sides \pi - A, \pi - B, \pi - C, and angles \pi - a, \pi - b, \pi - c.
There is a neat construction relating the two, which I can never remember how to do ...
I am indebted to two Russian gentlemen by the name of A. Zaslavskiy and M. Skopenkov for the reminder that the dual triangle is "a triangle such that the vectors pointing to its vertices are orthogonal to the planes containing the sides of the initial triangle". Y'know, Bill, I rather think everybody else must have gone on vacation. Bill? WFL